But then this contradicts what I've read before, that the keyblade of heart is required to open the door to Kingdom Hearts since the Keyblade War.
I think you misunderstand. There are three kinds of Keyblades.
"Keyblades of Light" are Keyblades that exist within the Realm of Light.
"Keyblades of Darkness" are Keyblades that exist in the Realm of Darkness.
"Keyblades of People's Heart" are Keyblades created by forcing hearts together.
The Keyblade of heart is a Keyblade created by forcing the hearts of the Princesses of Heart together. The X-Blade is also considered a Keyblade of People's Heart because it is created by clashing hearts of equal light and darkness against each other.
These both can access Kingdom Hearts, but one will open the Door of Darkness where Kingdom Hearts lies within and the other will open the pathway to Kingdom Hearts directly, essentially bring Kingdom Hearts to the person who called it.
But then how does the keyblade of heart tie in with this?
Keyblade of heart is just one way to reach Kingdom Hearts, but it is not the proper way. It only opens the Door to Darkness and Kingdom Hearts has to be found within the Darkness.
The X-Blade is the correct way to reach Kingdom Hearts. It bypasses the Realm of Darkness and goes straight to Kingdom Hearts itself. An imperfect X-Blade will not open the path, though. 20 hearts must clash to reach it in its proper form (7 lights vs 13 darknesses).
Xehanort was fine with creating artificial versions of Kingdom Hearts to reach the same ends, though, but his plans failed both times. The Kingdom Hearts in KH1 was the Kingdom Hearts SoD created by destroying worlds to force a Kingdom Hearts born of worlds into existence, and Xemnas created a Kingdom Hearts born of the hearts of man.
This is why Xehanort wants to reach the true Kingdom Hearts now. His plans to force one into creation failed, so he needs the real one to reach his goals.